In an aircraft flight control system employing model-following control laws, aircraft coordinates measured around the pitch, roll and yaw axes of the aircraft are transformed from aircraft body coordinates into inertial referenced (Euler) coordinates, processed, and re-transformed into body coordinates, as shown in U.S. Pat. No. 5,169,090. Various altitude and attitude rate signals are used in the transformation.
A typical model-following control system employs values of the cosine and tangent of the aircraft pitch attitude angle, .theta.. In highly maneuverable aircraft, including new generation attack helicopters, certain maneuvers, such as a symmetric loop or a split S, result in a pitch angle approaching plus 90.degree. (toward the zenith) or minus 90.degree. (toward the nadir). When pitch attitude, .theta., approaches 90.degree., cos .theta. approaches zero and values of 1/cos(-.theta.) and tan .theta. approach infinity. Thus, the transformation is bounded. When the aircraft passes through either zenith or nadir, roll attitude and heading change by 180.degree. instantaneously.
In the aforementioned patent, whenever the pitch axis angle approaches plus or minus degrees, the model (of each model-following attitude control channel), protects against Euler singularities by driving the model toward the sensed attitude quickly. This in turn drives the corresponding attitude error to zero, resulting in no trim signal being sent to the rotors from the automatic flight control system. Further, when the related sensed attitude is itself a singularity error (180.degree. flipped), the result changes from an error of zero to an extremely large error essentially instantaneously, as the Euler protection is removed, upon reaching a lower pitch attitude.